Automatic test data generation leads to the identification of input values on which a selected path or a selected branch is executed within a program (path-oriented vs goal-oriented methods). In both cases, several approaches based on constraint solving exist, but in the presence of pointer variables only path-oriented methods have been proposed. Pointers are responsible for the existence of conditional aliasing problems that usually provoke the failure of the goal-oriented test data generation process. In this paper, we propose an overall constraint-based method that exploits the results of an intraprocedural points-to analysis and provides two specific constraint combinators for automatically generating goal-oriented test data. This approach correctly handles multi-levels stack-directed pointers that are mainly used in C programs. The method has been fully implemented in the test data generation tool INKA and first experiences in applying it to a variety of existing programs are presented.